Settling times

While the manufacturers of measurement devices can supply some information on the dynamic characteristics of their devices, interpretation is often difficult. Measurement device dynamics are quoted on varying bases, such as rise time, time to 63 percent response, settling time, and so on. Even where the time to 63 percent response is quoted, it might not be safe to assume that the measurement device exhibits first-order behavior. 

Besides looking at just the mixing, it is important at this time to also consider the settling time of the phases after mixing since this will impact on the settler design. Higher intensity of mixing may decrease the residence time for mass transfer, but at the same time create fine dispersions which are difficult to settle. 

A second, direct approach which yields a similar result, since it also takes compression into account, utilizes the value of settling time... 

If there is water to be settled and withdrawn from hydrocarbon, the water s settling time requirement needs to be checked. The water settling requirement, rather than other process considerations, might set the liquid surge capacity. Therefore, the liquid surge capacity we have previously estimated from tables might have to be increased. 

Specification The CNC machine-table control system is to be critically damped with a settling time of 0.1 seconds. 

Control problem To select the controller gain K to achieve the settling time and tachogenerator constant to provide critical damping. 

Calculation of K In general, the settling time of a system with critical damping is equal to the periodic time of the undamped system, as can be seen in Figure 3.19. This can be demonstrated using equation (3.62) for critical damping... 

Control problem For a speeifie hull, the eontrol problem is to determine the autopilot setting K ) to provide a satisfaetory transient response. In this ease, this will be when the damping ratio has a value of 0.5. Also to be determined are the rise time, settling time and pereentage overshoot. 

It ean be seen in Figure 5.17 that the pole at the origin and the zero at. v = —1 dominate the response. With the eomplex loei, ( = 0.7 gives K a value of 15. ITowever, this value of K oeeurs at —0.74 on the dominant real loeus. The time response shown in Figure 5.20 shows the dominant first-order response with the oseillatory seeond-order response superimposed. The settling time is 3.9 seeonds, whieh is outside of the speeifieation. 

The root locus diagram is shown in Figure 5.19. In this case the real locus occurs between. v = —5 and —3 and the complex dominant loci breakaway at rrh = —1-15. Since these loci are further to the right than the previous option, the transient response will be slower. The compensator gain that corresponds to ( = 0.7 is K = 5.3. The resulting time response is shown in Figure 5.20, where the overshoot is 5.3% and the settling time is 3.1 seconds. 

Without stabilization, the step response of the roll dynamies produees a 45% overshoot and a settling time of 10 seeonds. The stabilization eontrol system is required to provide a step response with an overshoot of less than 25%, a settling time of less than 2 seeonds, and zero steady-state error. 

Thus the settling time is inversely proportional to the bandwidth. Comparing equation (6.70) with equation (3.68) gives... 

Equation (7.63) results in a polar diagram in the z-plane as shown in Figure 7.16. Figure 7.17 shows mapping of lines of constant a (i.e. constant settling time) from the. V to the z-plane. From Figure 7.17 it can be seen that the left-hand side (stable) of the. v-plane corresponds to a region within a circle of unity radius (the unit circle) in the z-plane. 

If there are unaeeeptable errors at time t, beeause of the dynamies of the plant, these will be as a result of eontrol aetion taken d seeonds previously, or at time t — d). The parameter r/ is a delay in reward parameter and is related to the settling time of the plant, having a typieal value of between iT and 5T, where T is the dominant time eonstant of the plant. 

If, for a given heterogeneous system, the settling veloeity of the smallest particles that will separate out is u and the height of the ehamber (or the distanee between horizontal plates) is H, then the settling time will be H/u. The time required for a... 

Look closely at the settling times in Table 1 - the times span from a fraction of a second to almost a lifetime A great deal of the suspended matter found in waste waters fall into the colloidal suspension range, so obviously we caimot rely on gravitational force alone to separate out the pollutants. 

Operating principle. Particles of terminal velocity Vi > mq will tend to settle therefore design for Vi < mq of the smallest particle present in the feed stream. In other words, the settling time should be less than the mean residence time of the up-flowing fluid. 

The settling rate and settling time ean be estimated using e.g. the Riehardson and Zaki equation (2.42). For slurries of irregular partieles, however, the assumptions in the eorrelation are exeeeded and the settling rate then beeomes more diffieult to ealeulate. Consequently, the Jar Test (see Chapter 2) is frequently used to determine R and /r in praetiee. 

Therefore, if /i [Pg.110]

Now, partieles will separate out if the settling time is less than the mean residenee time of the fluid i.e. 

Absetz-zeit, /. settling time, -zisteme, /, settling cistern. 

Let the mud circulate through all pits (tanks) available to increase the settling time do not agitate the mud. 

Three factors must be considered when acquiring vibration data settling time, data verification, and additional data that may be required. 

---